international journal of refrigerationmbahrami/pdf/2018/thermal conductivity... · rezk and...

ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

International Journal of Refrigeration 0 0 0 (2018) 1–11

Contents lists available at ScienceDirect

International Journal of Refrigeration

journal homepage: www.elsevier.com/locate/ijrefrig

Thermal conductivity of AQSOA FAM-Z02 packed bed adsorbers in

open and closed adsorption thermal energy storage systems

Mina Rouhani, Wendell Huttema, Majid Bahrami ∗

Laboratory for Alternative Energy Conversion (LAEC), School of Mechatronic Systems Engineering, Simon Fraser University, BC V3T0A3, Canada

a r t i c l e i n f o

Article history:

Available online xxx

Keywords:

Effective thermal conductivity

Thermal contact resistance

AQSOA FAM-Z02

Packed bed adsorber

Closed and open adsorption systems

Adsorption thermal energy storage

a b s t r a c t

In this study, the effective thermal conductivity (ETC) of uniformly-sized packed bed adsorber is mod-

eled as a function of water uptake, number of adsorbent layers, particle size, bed porosity, tempera-

ture, contact pressure, and interstitial gas pressure. The model is validated against experimental data

for 2 mm AQSOA FAM-Z02, measured by heat flow meter method (ASTM standard C518), and the max-

imum relative differences between the predicted values and the experimental data are 2% for ETC and

8% for total thermal conductivity. For 0.32 kg kg ads −1 water uptake, at 30 °C, ETC of an open-system

2 mm FAM-Z02 SC-arranged packed bed adsorber is 2.2 times higher than the ETC of a closed-system

(0.1031 W m

−1 K

−1 compared to 0.0474 W m

−1 K

−1 ). ETC charts are presented based on the equilibrium

water uptake isotherms for 0.5 and 2 mm FAM-Z02 packed beds, which provides a detailed and clear

picture of ETC of packed bed adsorbers for both open and closed thermal energy storage applications.

For each packed bed storage volume, an optimum particle size can be predicted by the presented model,

which ensures the highest packed bed total thermal conductivity.

© 2018 Elsevier Ltd and IIR. All rights reserved.

Conductivité thermique des adsorbeurs à garnissage AQSOA FAM-Z02 dans les

systèmes ouverts et fermés de stockage d’énergie thermique par adsorption

Mots-clés: Conductivité thermique efficace; Résistance thermique de contact; AQSOA FAM-Z02; Adsorbeur à garnissage; Systèmes à adsorption fermés et ouverts; Stockage

d’énergie thermique par adsorption

1

s

(

e

2

t

W

r

b

s

i

m

t

b

e

m

o

p

m

p

s

a

t

f

h

0

. Introduction

To reduce primary energy demand and greenhouse gas emis-

ions, adsorption systems, including adsorptive heat transformers

Frazzica et al., 2014; Freni et al., 2015 ) and adsorption thermal

nergy storage (ATES) systems ( Li et al., 2014 ; Schreiber et al.,

015 ), have received increased attention in recent years. However,

he low thermal conductivity of adsorbent materials, 0.1–0.8

m

−1 K

−1 ( N’ Tsoukpoe et al., 2014 ), and high thermal contact

esistance (TCR) between the adsorbent materials and adsorber

ed metal surfaces suppress the overall performance of adsorption

ystems, through slow desorption and adsorption processes. To

nvestigate and improve the heat transfer performance of adsorp-

∗ Corresponding author.

E-mail addresses: [email protected] (M. Rouhani), [email protected] (W. Huttema),

[email protected] (M. Bahrami).

e

p

i

m

ttps://doi.org/10.1016/j.ijrefrig.2018.05.012

140-7007/© 2018 Elsevier Ltd and IIR. All rights reserved.

Please cite this article as: M. Rouhani et al., Thermal conductivity of AQ

tion thermal energy storage systems, International Journal of Refrigerat

ion systems, effective thermal conductivity (ETC) of the adsorber

eds as well as the TCR, should be measured and modeled prop-

rly. Since it is costly and difficult to run thermal conductivity

easurements in large-scale for varying particle size, number

f layers, filling gas pressure, relative humidity (RH), contact

ressure, water uptake and temperature, a reliable comprehensive

odel for thermal conductivity is vital to accurately analyze,

redict, and improve the thermal performance of adsorption

ystems.

Exploiting heat sources with intermittent nature (e.g. renew-

bles and waste heat) and matching it with the demand side make

hermal energy storage (TES) an effective method for reducing the

ossil fuel dependency and carbon emissions ( Cabeza, 2014 ). High

nergy storage density, low heat loss and using non-toxic and non-

olluting refrigerants make adsorption TES (ATES) more appeal-

ng and effective for heat/cold storage, compared to other ther-

al storage methods ( Cabeza, 2014; Yu et al., 2013 ). Packed bed

SOA FAM-Z02 packed bed adsorbers in open and closed adsorp-

ion (2018), https://doi.org/10.1016/j.ijrefrig.2018.05.012

https://doi.org/10.1016/j.ijrefrig.2018.05.012

http://www.ScienceDirect.com

http://www.elsevier.com/locate/ijrefrig

mailto:[email protected]





2 M. Rouhani et al. / International Journal of Refrigeration 0 0 0 (2018) 1–11

ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

a

2

e

t

f

i

l

r

m

t

f

T

t

s

e

o

i

t

e

o

t

(

d

a

R

i

s

p

Nomenclature

A heat transfer surface area of the packed bed, m

2

A cell heat transfer surface area of the unit cell, m

2

ATES adsorption thermal energy storage

a macro radius of macro-contact, mm

a H radius of Hertzian contact, mm

αT thermal accommodation coefficient

b macro chord of macro-contact, mm

β volume fraction

d p adsorbent particle diameter, mm

d v Vickers indentation diagonal, μm

ɛ adsorbent particle porosity

E p Young’s modulus of adsorbent particle, GPa

ETC effective thermal conductivity

F contact force, N

FCC face center cubic arrangement

k thermal conductivity, W m

−1 K

−1

k eff, bed packed bed effective (medium) thermal conductivity

(effects of TCR is not included.), W m

−1 K

−1

k eff, FCC FCC-arranged packed bed effective thermal conduc-

tivity (effects of TCR is not included.), W m

−1 K

−1

k eff, SC SC-arranged packed bed effective thermal conduc-

tivity (effects of TCR is not included.), W m

−1 K

−1

k g adsorbate gas thermal conductivity, W m

−1 K

−1

k ha humid air thermal conductivity, W m

−1 K

−1

k p adsorbent particle thermal conductivity, W m

−1 K

−1

k tot packed bed total thermal conductivity (effects of

TCR is included.), W m

−1 K

−1

k v water vapour thermal conductivity, W m

−1 K

−1

L b−cell boundary unit cell length, mm

L bed packed bed length (thickness), mm

L cell unit cell length, mm

m number of adsorbent particles in each adsorbent

layer

m ads adsorbent mass, kg

n number of layers of adsorbent particles

r adsorbent particle radius, mm

ρp radius of adsorbent sphere, m

−1

ρs density of solid adsorbent, kg m

−3

ρw

density of adsorbate water, kg m

−3

νp Poisson’s ratio of adsorbent particle

ω water uptake, kg kg ads −1

ω eq equilibrium water uptake, kg kg ads −1

P gas pressure, Pa

P 0 maximum contact pressure, Pa

P ′ 0 relative maximum contact pressure, Pa

P 0, H Hertzian pressure, Pa

P ref reference gas pressure, Pa

P contact contact pressure at the contact of adsorbent particle

and the metal surface, Pa

P sat saturation pressure, Pa ˙ Q heat flow, W

˙ Q C,macro macro-contact heat flow, W

˙ Q c,micro micro-contact heat flow, W

˙ Q g,micro micro-gap heat flow, W

˙ Q G,macro macro-gap heat flow, W

R thermal resistance, K- W

−1

R bed packed bed medium thermal resistance (effect of

TCR is not included), K W

−1

R cell unit cell thermal resistance, K W

−1

R C, macro macro-contact thermal resistance, K W

−1

R c, micro micro-contact thermal resistance, K W

−1

fi



R g, micro micro-gap thermal resistance, K W

−1

R G, macro macro-gap thermal resistance, K W

−1

R p adsorbent particle thermal resistance, K W

−1

R tot packed bed total thermal resistance (effect of TCR is

included), K W

−1

RH relative humidity, %

SC simple cubic arrangement

ψ bed packed bed solid fraction

ψ FCC FCC-arranged packed bed solid fraction

ψ SC SC-arranged packed bed solid fraction

T temperature, K

TCR thermal contact resistance, K W

−1

Subscripts

a air

ads adsorbent

bed packed bed

cell cell

closed closed sorption storage system

contact at the contact of adsorbent particles and the heat

exchanger metal surface

eff effective

FCC FCC arrangement

g adsorbate gas

ha humid air

open open sorption storage system

p adsorbent particle

s solid particle (adsorbent skeleton)

SC SC arrangement

tot total

v water vapour

w water

wet wet adsorbent particle

dsorbers are widely used in adsorption systems ( Aristov et al.,

012; El-Sharkawy et al., 2013; Pistocchini et al., 2016; Ramzy K

t al., 2011; Hauer and Fischer, 2011; Palomba et al., 2017 ), since

hey provide higher cooling/heating energy per volume and benefit

rom lower cost and complexity, compared to the coated or consol-

dated adsorber beds ( Freni et al., 2015; Freni et al., 2015 ). A mono-

ayer configuration of adsorption beds ensures less heat transfer

esistance and higher water uptake rate, although multi-layers are

ore desirable for storage applications, due to the higher metal-

o-adsorbent mass ratio (active mass) and lower coefficient of per-

ormance of the monolayer configuration ( N’ Tsoukpoe et al., 2014 ).

hese two competing trends indicate a need for further investiga-

ion to establish optimum configurations (number of layers of ad-

orbents and packed bed arrangements).

Importance of TCR in adsorber beds has been raised in the lit-

rature ( Rezk et al., 2013; Li et al., 2015; Sharafian et al., 2014 ), but

nly adsorbent thermal conductivity or adsorber bed ETC are taken

nto account in most adsorption models. In the lumped-parameter

hermodynamic models, heat transfer in the adsorber bed heat

xchanger is modeled through an overall heat transfer coefficient

f the heat exchanger, and adsorption rate constant represents

he heat and mass transfer performance of an adsorption system

Alsaman et al., 2017 ). Mohammed et al. (2017) developed a three-

imensional local thermal non-equilibrium model, where ETC was

ssumed constant. In other theoretical models ( Riffel et al., 2010;

ezk and Al-Dadah, 2012 ), measured TCR values from the exper-

ments were fed into the model. Rezk and Al-Dadah (2012) pre-

ented a lumped analytical model for predicting ETC of a silica gel

acked bed, where they used a correlation for the TCR, which was

tted to the measured TCR in ref. Zhu and Wang (2002) .




M. Rouhani et al. / International Journal of Refrigeration 0 0 0 (2018) 1–11 3

ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

t

a

m

(

p

a

n

G

t

t

m

fi

a

c

t

w

a

c

e

a

t

i

c

w

t

r

t

e

w

t

i

(

o

c

f

s

a

e

t

o

m

c

p

b

b

t

p

p

m

v

2

r

b

B

a

m

T

a

B

i

M

2

t

b

(

t

t

a

c

c

p

h

b

t

c

w

w

t

m

m

u

o

∑

w

t

β

w

p

c

u

b

m

t

s

r

t

g

g

A

(

c

(

m

f

d

i

T

Y

a

P

B

Analytical and numerical solutions to the Laplace’s equation are

he first type of ETC models ( VDI Heat Atlas 2010 ). Maxwell an-

lytical solution, which is based on the assumption of no ther-

al influence between individual particles, falls in this category

VDI Heat Atlas 2010 ). On the other hand, numerical models of

acked bed thermal conductivity, which do not need such limiting

ssumptions, suffer from high computational cost and time.

Another type of ETC models is introducing thermal resistance

etwork for the packed bed adsorber ( VDI Heat Atlas 2010 ).

riesinger et al. (1999) experimentally and theoretically studied

he ETC of zeolite powder at atmospheric pressure by introducing

hree main parallel heat transfer paths (pure solid, pure fluid, and

ixed solid-fluid paths) and defining tuning parameters through

tting the theoretical curve to the measured values ( Griesinger et

l., 1999 ). Similarly, Dawoud et al. (2011) developed a model to cal-

ulate the ETC of wetted zeolite 4A, assuming an isotropic distribu-

ion of adsorbed water inside the zeolite crystal. A tortuosity factor

as defined for conductive heat transfer and their model took into

ccount the Knudsen conductivity of the vapor phase through the

urve fitting to their experimental data ( Dawoud et al., 2011 ). Nev-

rtheless, ETC models of small amount of adsorbent samples, i.e.

n adsorbent particle or powder, may not be an accurate represen-

ative of a large-scale packed bed adsorber, since they do not take

nto account all the thermal resistances inside the packed bed, in-

luding the thermal resistance between the adsorbent particles as

ell as the TCR.

Thermal conductivity modeling of a unit cell (as a represen-

ative of the repeating units in a packed bed), by using thermal

esistance network or basic models such as Maxwell, is another

ype of ETC models for packed beds ( VDI Heat Atlas 2010 ). Luikov

t al. (1968) defined a thermal resistance circuit for a unit cell,

hich contained a solid skeleton and surrounding gas, although

he boundary unit cell and water uptake were not considered

n their study. In addition to their model, Sarwar and Majumdar

1995) took into account the effects of the adsorbent water content

n a packed bed ETC, although interstitial gas pressure and the

ontact pressure were not considered as variables in their model.

Bahrami et al. (2006) developed an analytical unit-cell model

or ETC of uniformly-sized packed beds with high-conductive

pheres. Rouhani and Bahrami (2018) used their analytical model

s a platform for dry packed beds, and extended it to consider the

ffects of water uptake in the packed bed adsorbers. In this work,

he developed model in ref. Rouhani and Bahrami (2018) , inclusive

f considering the effects of air relative humidity on the air ther-

al conductivity of the open systems, is used to investigate and

ompare open and closed-system packed bed ATES systems. The

resent model can predict the ETC and TCR of packed bed adsor-

ers as a function of:( i) numbers of adsorbent layers, (ii) adsor-

ent properties, (iii) particle size, (iv) water uptake, (v) tempera-

ure, (vi) contact pressure, (vii) particles surface roughness, (viii)

article arrangement and (ix) interstitial gas pressure. This model

rovides a practical tool to analysis, optimize and compare ther-

al performances of open and closed packed bed adsorbers, under

arious operating conditions.

. Theoretical model

A unit cell approach is adopted, considering a unit-cell as the

epresentative of a uniformly-arranged simple cubic (SC) packed

ed, as shown in Fig. 1 a. In contrast to the model presented by

ahrami et al. (2006) , which was for high conductive particles,

dsorbent particle thermal resistance is considered in the present

odel, due to the high thermal resistance of adsorbent materials.

hermal conductivities of wet adsorbent particles are modeled by

n effective-medium approximation of multi-component systems,

ruggeman’s method.



Natural convection in the small voids between the particles

n the packed beds can be neglected ( Tsotsas and Martin, 1987 ).

oreover, in the model and the experimental data ( Rouhani et al.,

018 ), the heat flow is downward to eliminate the natural convec-

ion ( Incropera et al., 2007; Czichos et al., 2011 ). In the packed

eds for low-temperature applications radiation is also negligible

Yovanovich, 2003 ). Therefore, heat transfer occurs via conduction

hrough the solid adsorbent and conduction through the intersti-

ial gas, as shown in Fig. 1 b. These conductive heat transfer mech-

nisms take place in multi-scales: (i) macroscale, including macro-

ontact ( ˙ Q C,macro ) and macro-gap ( ˙ Q G, macro ) paths; and (ii) mi-

roscale, including micro-contact ( ˙ Q c,micro ) and micro-gap ( ˙ Q g, micro )

aths.

It is assumed that the steady-state condition is reached for both

eat and mass transfer; therefore, the water uptake of the adsor-

ent particles is corresponded to the equilibrium water uptake at

he steady-state temperature and pressure ratio ( P/ P sat@ T ads ).

A wet adsorbent particle is an inhomogeneous medium of three

omponents: (i) solid particle (adsorbent skeleton), (ii) adsorbed

ater on the surface of adsorbent pores, and (iii) interstitial gas,

hich is the air in the open adsorption systems and water vapor in

he closed adsorption systems. Among various models of effective-

edium approximation, Bruggeman’s method for multi-component

edium is selected, since it is readily applicable to arbitrary vol-

me fractions ( Stroud, 1998 ). Therefore, the thermal conductivity

f a wet adsorbent particle, k p, wet , can be calculated as follows,

3

i =1

βi

k i − k p,wet

k i + 2 k p,wet = 0 , where

3 ∑

i =1

βi = 1 (1)

here β i is the volume fraction of each component. Volume frac-

ion of solid particle, water and gas are obtained from Eq. (2) .

βs = 1 − ε

w

= ω

ρs

ρw

( 1 − ε )

βg = ε − ω

ρs

ρw

( 1 − ε ) (2)

here ɛ is the porosity of the adsorbent particle and ρs is the

ore-less density of the adsorbent material.

ETC of the packed bed adsorber is calculated based on the unit

ell approach and it is assumed that the heat conduction in the

nit cell is one dimensional, which leads to isothermal top and

ottom surfaces, while the lateral walls are adiabatic due to sym-

etry (see Fig. 1 a) ( Bahrami et al., 2006 ). As shown in Fig. 1 b, the

hermal resistance of the unit cell consists of: (1) bulk thermal re-

istance of particles, R p , (2) macro-contact constriction/spreading

esistance, R C, macro , (3) micro-contact constriction/spreading resis-

ance, R c, micro , (4) resistance of the interstitial gas in the micro-

ap, R g, micro , and (5) resistance of interstitial gas in the macro-

ap, R G, macro . The equations used in this study are presented in

ppendix A , and more details are found in ref. Bahrami et al.

2006) .

Thermal and physical properties of the adsorbent material, in-

luding thermal accommodation, αT, p , and Young’s modulus, E p see Appendix A ) are required for the ETC calculations. In this

odel, a clean surface is assumed for the adsorbent particle, there-

ore, the correlation for thermal accommodation of clean surfaces,

eveloped by Song and Yovanovich (1987) , is applied (see Eq. A 24

n Appendix A ). A thermomechanical analyzer (TMA Q400EM from

A Instruments) with precision of ± 0.1% was used to measure the

oung’s modulus of 2-mm FAM-Z02 adsorbent particle ( Rouhani

nd Bahrami, 2018 ). The value of 0.5736 GPa −1 was obtained for

( 1 − ν2 p ) / E p (see Eq. A 18 in Appendix A ), where νp is particles

oisson’s ratio and E p is particles Young’s modulus ( Rouhani and

ahrami, 2018 ). Using the proposed unit cell thermal resistance





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Fig. 1. (a) Packed bed adsorber of a dsorbents with diameter of d p , for simple cubic (SC) arrangement ( Bahrami et al., 2006 ), and (b) heat conduction in the packed bed,

shown in macro-scale and micro-scale, and a unit cell of a wet SC-arranged adsorber bed with the equivalent electrical circuit.

T

f

k

w

l

t

m

p

f

a

(

a

u

d

f

network, shown in Fig. 1 b, the total thermal resistance of the unit

cell is as follows,

R cell =

[

1 (1 / R c,micro + 1 / R g,micro

)−1 + R C,macro

+

1

R p + R G,macro

] −1

(3)

The unit cell ETC can be calculated from k e f f,cell =L cell / ( R cell A cell ) , which is also the ETC of the packed bed ( k eff, bed ),

considering a homogenous medium. Thermal resistances of the

unit cells along the bed’s length (i.e. in the heat transfer direction)

are in series, while they are parallel to each other in the direc-

tion perpendicular to the heat transfer path. Thus, the thermal

resistance of adsorber medium is R bed = [ L bed / ( k e f f,bed A cell ) ] /m ,

where L bed is the bed length in the heat transfer direction and m

is the number of unit cells in each layer of the adsorber bed.

The TCR in the unit cells adjacent to the two metal surfaces of

heat exchanger medium, are also in series with the medium re-

sistance ( R ). Thus, the total bed resistance is R tot = R + T CR .
bed bed


o this end, the total thermal conductivity of a packed bed can be

ound from:

tot =

L bed

A ( R bed + T CR ) (4)

here, A = A cell × m is the total area of the metal surface. Simi-

arly, all the thermal resistances of the adsorbent particle side and

he gas side are calculated for the face center cubic (FCC) arrange-

ent, using related equations in ref. Bahrami et al. (2006) and the

arameters in Table 1 , for FCC arrangement.

The ETC of a randomly packed bed ( ψ bed ≈ 0.6 ( Kaviany, 1995 ))

alls between that of the two uniformly-sized, uniformly-packed

rrangements: SC ( ψ bed = 0 . 524 ), as the lower bound, and FCC

ψ bed = 0 . 740) , as the upper bound ( Tien and Vafai, 1978; Karay-

coubian et al., 2005 ). Therefore, by assuming a linear relationship

sing the ETC values of SC and FCC arrangements, ETC of the ran-

omly packed bed can be estimated based on its solid fraction, as

ollows,

ψ bed − ψ SC

ψ F CC − ψ SC

=

k e f f,bed − k e f f,SC

k e f f,F CC − k e f f,SC

(5)





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Table 1

Specifications of SC and FCC arrangements of a packed bed.

Packing arrangement Solid fraction, ψ bed Bed length, L bed Cell area, A cell Cell length, L cell Boundary cell length, L b−cell

SC 0.524 n × d p d 2 p d p d p /2

FCC 0.740 ( ( n − 1 ) √

2 / 2 + 1 ) × d p d 2 p / 2 √

2 d p / 2 d p /2

Fig. 2. (a) Effective thermal conductivity and (b) total thermal conductivity of 4- and 6-layer packed beds versus temperature for 2-mm FAM-Z02 randomly packed beds

with the water uptake of 0.30 ± 0.02 kg kg ads −1 , at atmospheric condition and under contact pressure of 0.7 kPa. In the present model, ψ bed is 0.67.

Fig. 3. (a) Effective thermal conductivity of SG-arranged packed bed adsorber of 2 mm FAM-Z02 versus temperature, for open and closed-systems, at equilibrium water

uptake of 0.32 kg kg ads −1 and (b) the ratio of the macro-gap resistances of open-system to that of the closed-system.

w

a

f

0

k

c

2

3

3

(

r

here, ψ SC , ψ FCC and ψ bed are the solid fractions of the SC, FCC

nd any randomly packed bed arrangements, respectively. Solid

raction of a randomly packed bed adsorber can be assumed about

.62 (porosity of 0.38 ( Do, 1998 )) or can be chosen such that

eff, bed approaches the experimental data collected for thermal

onductivity of that randomly packed bed ( Rouhani and Bahrami,

018 ; Rouhani et al., 2018 ).

r

b

c

(

m

Z



. Results and discussion

.1. Model validation

The present ETC model is coded into MATLAB in four sections:

i) water uptake calculation from the equilibrium isotherms,

eported by Goldsworthy (2014) , (ii) adsorbent particle thermal

esistance model, (iii) packed bed cell resistance, and (iv) packed

ed boundary cell resistance models. The ETC model is then

ompared with the measured values of refs. Rouhani et al. (2018) ;

2016 ), where a heat flow meter (HFM) apparatus was used to

easure the total thermal conductivity of large-scale 2-mm FAM-

02 randomly packed beds, at adsorbent temperatures from 10 to





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Fig. 4. Effective thermal conductivity of closed-system FAM-Z02 packed bed adsorber versus water uptake, including the isotherm and isobar lines for (a) SC-arranged bed

with 0.5 mm adsorbent particles, (b) SC-arranged bed with 2 mm adsorbent particles, (c) randomly packed bed with 0.5 mm adsorbent particles, and (d) randomly packed

bed with 2 mm adsorbent particles.

t

s

8

t

i

e

a

t

T

m

d

w

b

t

2

p

T

d

w

80 °C. The packed beds were sandwiched between two aluminum

sheets and placed in the test chamber between two plates with

heat flow transducers in their center ( Rouhani et al., 2018 ). An ex-

ternal load was applied by the HFM on the packed bed, to control

the contact pressure and ensure a uniform contact between the

upper (hot)/lower (cold) plates and the packed adsorbent particles

( Rouhani et al., 2018; 2016 ). The comparison between the experi-

mental values and the present model for ETC is shown in Fig. 2 a,

for a 2-mm FAM-Z02 randomly packed bed. The black dashed line

represents the results of the present model, where the air thermal

conductivity is approximated as the thermal conductivity of dry

air, and the blue solid line shows the results from the model,

where the effect of RH changes on the air thermal conductivity is

also considered; thermal conductivity of humid air, as a function

of RH, is calculated from the equations presented in Table B1 of

Appendix B , using the mole-fraction-weighted mixing rule. As

shown in Fig. 2 a, the present model can predict k eff, bed accurately

and the agreement between the experimental data ( Rouhani et al.,

2018 ) and the results from the present model has been improved

by considering the effect of the RH changes, due to the tempera-



ure changes, on the air thermal conductivity; in the experimental

tudy ( Rouhani et al., 2018 ), RH was 25% (at 10 °C) and 80% (at

0 °C) for constant water uptake of 0.30 ± 0.02 kg kg ads −1 . For

emperatures above 60 °C and RH values above 50%, an increase

n RH decreases the thermal conductivity of humid air (see the

quation for k ha in Table B1 of Appendix B ). This decrease in the

ir thermal conductivity marginally decreases the ETC compared to

he case where the effects of the changes in RH are not considered.

he maximum relative difference between the results from the

odel without consideration of RH changes and the experimental

ata is 3% at 80 °C, while the maximum relative difference is 2%

ith consideration of RH changes at 80 °C. ETC of the packed

ed adsorber varies between 0.188 and 0.204 W m

−1 K

−1 . Total

hermal conductivities of the packed beds of 4 and 6 layers of

mm FAM-Z02 are shown in Fig. 2 b. The theoretical model can

roperly predict the total thermal conductivity, which includes the

CR as well. The maximum difference between the experimental

ata and the results from the theoretical model is 8% and lies

ithin the uncertainty of the measurements.





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Fig. 5. Effective thermal conductivity of open-system FAM-Z02 packed bed adsorbers versus water uptake, including the isotherm and isobar lines for (a) SC-arranged bed

with 0.5 mm adsorbent particles, (b) SC-arranged bed with 2 mm adsorbent particles, (c) randomly packed bed with 0.5 mm adsorbent particles, and (d) randomly packed

bed with 2 mm adsorbent particles.

3

p

2

a

(

a

3

0

c

t

s

s

(

t

p

r

i

3

b

p

a

F

a

w

f

G

i

f

f

p

w

a

c

a

.2. Effective thermal conductivity: open-system versus closed-system

acked bed adsorbers

ETCs of open and closed-system packed bed adsorbers of

mm FAM-Z02 at equilibrium water uptake of 0.32 kg kg ads −1 ,

re shown in Fig. 3 a. According to the water uptake isotherms

Goldsworthy, 2014 ), the RH changes from 25% to 80% for temper-

tures of 10 to 80 °C. As shown in Fig. 3 a, ETC of open-system is

.3 times as high as ETC of the closed-system (0.099 compared to

.030 W m

−1 K

−1 ) at 10 °C, and 1.2 times as high as that of the

losed system (0.107 compared to 0.090 W m

−1 K

−1 ) at 80 °C. Al-

hough the water uptake is kept the same for both open and closed

ystems, the gas pressure around the adsorbents in the closed-

ystem is much lower and varies from 331 Pa (at 10 °C) to 37,612 Pa

at 80 °C). The ratio of macro-gap resistances of the open-system

o that of the closed-system, in Fig. 3 b, shows that the low gas

ressure in the closed-system leads to relatively high macro-gap

esistances, especially at lower temperatures. The R G, open / R G, closed

s 0.23 at 10 °C (331 Pa) and 0.79 at 80 °C (37,612 Pa).



.3. Effective thermal conductivity chart for closed-system packed

ed adsorbers

The dependencies of the ETC on the water uptake, vapour

ressure, and mean temperature are shown in Fig. 4 for SC-

rranged and randomly packed beds ( ψ bed = 0 . 6 ) of 0.5 and 2 mm

AM-Z02. To consider the real effects of water uptake, pressure

nd temperature on the ETC in closed adsorption systems, the

ater uptake is calculated at each temperature and pressure ratio

rom the equilibrium uptake isotherms of FAM-Z02, presented by

oldsworthy (2014) . Afterwards, using the present model, the ETC

s obtained based on the pressure, temperature and water uptake,

orming the isobars and isotherms in Fig. 4 . ETCs are reported

or the temperatures of 10 to 90 °C, pressures of 873 (saturation

ressure at 5 °C) and 19,947 Pa (saturation pressure at 60 °C), and

ater uptakes of 0.03 to 0.33 kg kg ads −1 . As shown in Fig. 4 , at

fixed gas pressure, ETC does not significantly change with the

hanges in temperature and water uptake; at a constant pressure,

n increase in temperature leads to a decrease in the equilibrium





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Fig. 6. (a) ETC and (b) TCR · A of a closed-system SC-arranged packed bed adsorber versus contact pressure for various particle diameters, at 30 °C and 1706 Pa

( ω eq = 0.32 kg kg ads −1 ). L bed is fixed at 12 mm.

0

b

s

3

a

d

p

E

i

0

c

t

0

3

c

t

F

1

f

T

b

b

p

a

f

(

t

n

a

L

d

w

p

water uptake. Temperature rise increases the ETC, while water

uptake drop decreases the ETC. The tradeoff between these two

effects results in an almost constant ETC. However, at a fixed tem-

perature, equilibrium water uptake increases with an increase in

gas pressure and both increases positively affect the ETC. At 90 °C,

by increasing the gas pressure from 872 Pa ( ω eq = 0 . 03 kg kg ads −1 )

to 19,947 Pa ( ω eq = 0 . 26 kg kg ads −1 ), ETC increases from 0.027 to

0.068 W m

−1 K

−1 for 0.5 mm, and from 0.044 to 0.084 W m

−1 K

−1

for 2 mm SC-arranged packed beds. Considering the equilibrium

uptake isotherms, it can be concluded that ETC is a stronger

function of vapor pressure than temperature in closed systems,

for the studied temperature and pressure ranges. Higher thermal

conductivities have been predicted for randomly packed beds

compared to the SC-arranged beds, due to the lower bed porosity

of randomly packed beds, which makes thermal conductivity

of adsorbent particle to take higher part in the ETC; thermal

conductivity of the adsorbent, i.e. 0.117 W m

−1 K

−1 (at 30 °C)

and 0.128 W m

−1 K

−1 (at 90 °C) ( Kakiuchi et al., 2004 ), is higher

than that of the water vapor, i.e. 0.017 W m

−1 K

−1 (at 873 Pa) to

0.021 W m

−1 K

−1 (at 19,947 Pa) ( Wagner and Kretzschmar, 2008 ).

3.4. Effective thermal conductivity chart for open-system packed bed

adsorbers

Changes in ETC due to the water uptake, RH and mean tem-

perature in the open-system packed bed adsorbers are shown in

Fig. 5 , for SC-arranged and randomly packed beds of 0.5 and 2 mm

FAM-Z02 particles. Considering the equilibrium uptake of FAM-Z02,

the isorelative humidity lines and isotherms and their correspond-

ing water uptake and effective thermal conductivity are shown in

Fig. 5 . ETCs are reported for temperatures of 10 to 90 °C, RH of

5 to 40%, and water uptake of 0.06 to 0.33 kg kg ads −1 . ETCs in

the open systems are higher compared to the ETCs of the closed

systems, due to the higher pressure of the filling gas, which leads

to lower micro-gap and macro-gap resistances (see Eqs. A 4 and

A 5 in Appendix A ), and higher thermal conductivity of air com-

pared to that of the water vapour; At adsorbent temperature of

30 °C and water uptake of 0.32 kg kg ads −1 (i.e. water vapor sat-

uration temperature of 15 °C in closed-system, and RH of 40%

in open-system), ETC of 2 mm FAM-Z02 open-system randomly

packed bed is 0.149 W m

−1 K

−1 , while that of a closed-system is



.065 W m

−1 K

−1 , and ETC of 0.5 mm FAM-Z02 randomly packed

ed in an open-system is 0.126 W m

−1 K

−1 , while that of a closed-

ystem is 0.042 W m

−1 •K

−1 .

.5. Effect of contact pressure on the effective thermal conductivity

ETC and TCR · A versus the contact pressure are shown in Fig. 6 ,

t 30 °C and water uptake of 0.32 kg kg ads −1 for various particle

iameters. Increasing the contact pressure leads to better inter-

article contacts in the packed bed and, therefore, an increase in

TC (see Fig. 6 a). In contrast to ETC, TCR · A decreases with an

ncrease in the contact pressure, as shown in Fig. 6 b. For d p of

.25 mm ( d p / L bed = 0 . 02 ), the decrease in TCR · A due to the in-

rease in contact pressure from 0.7 to 1,0 0 0 kPa is 37%, from 0.006

o 0.004 K m

2 W

−1 , while this decrease for d p of 2 mm ( d p / L bed = . 17 ) is 31%, from 0.026 to 0.018 K m

2 W

−1 .

.6. Effect of particle size on the effective and total thermal

onductivity

As shown in Fig. 6 b, TCR increases with an increase in d p due

o the less contact points with the metal surface of heat exchanger.

or d p of 0.5 mm ( d p · L −1 bed

= 0 . 04 ) and under contact pressure of

00 kPa, TCR · A is 0.008 K m

2 W

−1 and TCR · R −1 tot is 0.023, and

or d p of 2 mm ( d p · L −1 bed

= 0 . 17 ), TCR · A is 0.022 K m

2 W

−1 and

CR · R −1 tot is 0.086. However, as shown in Fig. 6 a, ETC of a packed

ed of 0.5 mm FAM-Z02 is 0.039 W m

−1 K

−1 and that of a packed

ed of 2 mm FAM-Z02 is 0.055 W m

−1 K

−1 , at 30 °C and under gas

ressure of 1706 Pa and contact pressure of 100 kPa.

Total thermal conductivities of an open-system FAM-Z02 SC-

rranged packed bed versus the relative particle size, d p · L −1 bed

,

or bed thicknesses of 0.6 ( A · m

−1 ads

= 4.90 m

2 kg −1 ) to 48 mm

A · m

−1 ads

= 0.06 m

2 kg −1 ) are shown in Fig. 7 . For a constant bed

hickness, k tot of the packed beds with smaller d p · L −1 bed

(i.e. more

umber of particle layers) is close to the ETC of the packed bed,

nd both ETC and k tot increase with particle size. For higher d p ·

−1 bed

(i.e. less number of particle layers), the thermal contact con-

uctance plays a more important role in the k tot and decreases

ith an increase in the particle size, since the number of contact

oints decreases with particle size. Hence, an optimum particle





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Fig. 7. Total thermal conductivity of an open-system FAM-Z02 SC-arranged packed

bed at 30 °C and ω = 0.32 kg kg ads −1 .

Fig. 8. ETC of dry and wet open and closed-systems SC-arranged packed bed ad-

sorbers versus particle diameter for various gas pressures at adsorbent temperature

of 30 °C.

s

e

Z

A

fl

m

s

a

a

o

A

3

a

g

i

A

f

g

F

(

f

1

p

u

s

0

4

s

t

p

F

T

b

e

t

Z

T

s

i

2

t

c

t

w

f

t

e

p

t

F

0

8

o

o

4

0

t

(

m

t

n

fl

s

a

v

A

t

(

A

A

m

ize is observed for each bed thickness, which provides the high-

st k tot . For instance, for 2 mm bed thickness, the optimum FAM-

02 particle diameter which provides the highest k tot is 0.34 mm.

s raised by N’Tsoukpoe et al. (2014) , predicting the optimum heat

ow and mass flow path lengths for a certain bed volume is im-

ensely beneficial for design and optimization of packed bed ad-

orbers. The presented model, which takes into account the TCR

s well as the ETC for large-scale packed bed adsorbers, provides

reliable tool to predict the optimum heat flow path size (i.e. the

ptimum particle size) for a certain packed bed storage volume in

TES systems.

.7. Effect of gas pressure on the thermal conductivity

As shown in Fig. 8 , ETC of a dry and wet closed-system SC-

rranged FAM-Z02 packed bed increases with an increase in the

as pressure. Increasing the gas pressure leads to a decrease



n the mean free path of the interstitial gas (see Eq. A 23 in

ppendix A ) and, therefore, an increase in the ETC. Moreover,

or wet packed beds, the equilibrium uptake is higher at higher

as pressures, which also leads to an increase in ETC. In a wet

AM-Z02 packed bed, by decreasing the gas pressure from 4247

P sat at 30 °C) to 1706 ( P sat at 15 °C) Pa, ETC decreases by 23%,

rom 0.043 to 0.033 W m

−1 K

−1 , for 0.5 mm particles, and by

6%, from 0.057 to 0.048 W m

−1 K

−1 , for 2 mm particles. For

article diameter of 0.5 mm, ETC of an open-system packed bed

nder RH of 40% is 0.079 W m

−1 K

−1 , while that of a closed

ystem is 0.031 W m

−1 K

−1 at vapour pressure of 1706 Pa, and

.040 W m

−1 K

−1 at vapour pressure of 4247 Pa.

. Conclusions

In this study, the effective thermal conductivity of uniformly-

ized packed bed adsorber was modeled as a function of water up-

ake, number of adsorbent layers, particle size, bed porosity, tem-

erature, contact pressure, and interstitial gas pressure for SC and

CC arrangements, which was extended to randomly packed beds.

he model was validated with the experimental results, collected

y heat flow meter measurements, with a maximum relative differ-

nce of 2% for ETC and 8% for total thermal conductivity. The effec-

ive thermal conductivity of a randomly packed bed of 2 mm FAM-

02 was between 0.188 (at 10 °C) and 0.204 W m

−1 K

−1 (at 80 °C).

he comparison between the ETC of open-system and closed-

ystem packed bed adsorbers showed that ETC of the open-system

s higher than the ETC of the closed system. For instance, ETC of

mm FAM-Z02 SC-arranged open-system is 2.2 times higher than

he ETC of the closed-system at 30 °C and 0.32 kg kg ads −1 (0.1031

ompared to 0.0474 W m

−1 K

−1 ). For more realistic analysis of

he heat transfer inside the packed bed adsorbers, the ETC charts

ere presented based on the equilibrium water uptake isotherms

or both open and closed systems. Considering the dependencies of

he water vapour pressure, temperature and water uptake by the

quilibrium uptake isotherm, changes in ETC with water vapour

ressure and water uptake were higher than its changes with

he temperature in the closed systems; for 0.5 mm SC-arranged

AM-Z02 bed at 90 °C, ETC increased by 2.5 times from 0.027 to

.068 W m

−1 K

−1 when water vapour pressure increases from

73 Pa (water saturation temperature of 5 °C and water uptake

f 0.03 kg kg ads −1 ) to 19,947 Pa (water saturation temperature

f 60 °C and water uptake of 0.26 kg kg ads −1 ). However, under

247 Pa (water saturation temperature of 30 °C), ETC changed from

.044 W m

−1 K

−1 to 0.50 W m

−1 K

−1 when adsorbent tempera-

ure increased from 10 °C (water uptake of 0.33 kg kg ads −1 ) to 90 °C

water uptake of 0.08 kg kg ads −1 ). Moreover, it was shown that the

odel could predict an optimum particle size that corresponded

o the highest total thermal conductivity for a certain bed thick-

ess, which should be considered, along with the optimum mass

ow path size, for the design and optimization of packed bed ad-

orbers; for instance, considering 2 mm thickness for a FAM-Z02

dsorber packed bed, the optimum particle diameter which pro-

ides the highest k tot is 0.34 mm.

cknowledgements

The authors gratefully acknowledge the financial support of

he Natural Sciences and Engineering Research Council of Canada

NSERC) through the Automotive Partnership Canada Grant no.

PCPJ 401826–10 .

ppendix A

The equations which are used in the present model to find the

icro/micro-contact and micro/macro-gap resistances are listed in





ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

Table A1

Equations used to find the thermal resistance of the unit cell, R cell , ( Bahrami et al., 2006 ; Song and Yovanovich, 1987 ).

Equations Eq. number Ref.

R cell = [ 1

( 1 / R c,micro +1 / R g,micro ) −1 + R C,macro

+

1 R p + R G,macro

] −1 K W

−1 A 1 Bahrami et al. (2006)

R c,micro = [ 0 . 565 H micro ( σp / m p ) ] / ( k s F ) K W


R C,macro = 1 / ( 2 k s a macro ) K W


R g,micro = ( 2 √

2 σp a 2 ) / { π k g a 2 macro ln ( 1 +

a 2 a 1 + M/ [ 2

√ 2 σp ]

) } K W


R G,macro =

2

π k g [ S ln ( S−B S−A )+ B −A ]

K W


k s =

2 k p, 1 k p, 2

k p, 1 + k p, 2 W m

−1 K −1 A 6 Bahrami et al. (2006)

H micro = c 1 ( d v / σ0 ) c 2 Pa A 7 Bahrami et al. (2006)

σ0 = 1 μm , d v = 0 . 95( σp / m p ) M A 8 Bahrami et al. (2006 ; Hegazy (1985)

c 1 = H BGM ( 4 . 0 − 5 . 77 κ + 4 . 0 κ2 − 0 . 61 κ3 ) , κ = H B / H BGM Pa A 9 Bahrami et al. (2006)

c 2 = −0 . 57 + 0 . 82 κ − 0 . 41 κ2 − 0 . 06 κ3 A 10 Bahrami et al. (2006)

H BGM = 3 . 178 GPa , 1.3 ≤ H B ≤ 7.6 GPa Pa A 11 Bahrami et al. (2006)

m p =

√

m

2 p1

+ m

2 p2

, m p1 = 0 . 076 σ 0 . 52 p1 A 12 Bahrami et al. (2006)

σp =

√

σ 2 p1

+ σ 2 p2

M A 13 Bahrami et al. (2006)

a macro

a H = { 1 . 605 /

√

P ′ 0 0 . 01 ≤ P ′ 0 ≤ 0 . 47

3 . 51 − 2 . 51 P ′ 0 0 . 47 ≤ P ′ 0 ≤ 1 A 14 Bahrami et al. (2006)

P ′ 0 = P 0 / P 0 ,H = 1 / ( 1 + 1 . 37 α( ρp / a H ) −0 . 075

) , α =

σp ρp

a 2 H

A 15 Bahrami et al. (2006)

P 0 ,H = 1 . 5 F/ ( πa 2 H ) Pa A 16 Bahrami et al. (2006)

a H = ( 0 . 75 F ρp /E ′ ) 1 / 3 M A 17 Bahrami et al. (2006)

E ′ = [ ( 1 − ν2 p1 ) / E p1 + ( 1 − ν2

p2 ) / E p2 ] −1 Pa A 18 Bahrami et al. (2006)

ρp = ( 1 / ρp1 + 1 / ρp2 ) −1 M A 19 Bahrami et al. (2006)

a 1 = erf c −1 ( 2 P 0 /H ′ ) , a 2 = erf c −1 ( 0 . 003 P 0 /H ′ ) − a 1 A 20 Bahrami et al. (2006)

H ′ = c 1 ( 1 . 62( σp / σ0 ) / m p ) c 2 GPa A 21 Bahrami et al. (2006)

M = ( 2 −αT1

αT1 +

2 −αT2

αT2 )(

2 γg

1+ γg ) 1

Pr M A 22 Bahrami et al. (2006)

=

P re f

P g

T g T re f

re f , ref : mean free path value at reference gas temperature T ref and pressure P ref M A 23 Bahrami et al. (2006)

αT = exp [ −0 . 57( T s −T re f

T re f ) ]( M ∗

6 . 8+ M ∗ ) +

2 . 4 μ

( 1+ μ) 2 { 1 − exp[ −0 . 57(

T s −T re f

T re f ) ] } , μ = M g / M s A 24 Song and Yovanovich (1987 )

M

∗ = { M g monoatomic gas

1 . 4 M g diatomic / polyatomic gas kg mol −1 A 25 Song and Yovanovich (1987 )

A = 2 √

ρ2 p − a 2 macro , B = 2

√

ρ2 p − b 2 macro , S = 2( ρp − ω 0 ) + M, ω 0 = a 2 macro / ( 2 ρp ) m A 26 Bahrami et al. (2006)

Table B1

Thermal conductivity of air and water vapour.

Thermal conductivity, W m

−1 K −1

Dry air k a 0 . 00243 + 7 . 8421 × 10 −5 T ( ◦C ) − 2 . 0755 × 10 −5 T ( ◦C ) 2 VDI Heat Atlas (2010)

Water vapour k v 1 . 713 ×10 −4 ( 1+0 . 0129 T (K) )

√

T (K)

1 −[ 80 . 95 /T (K) ] VDI Heat Atlas (2010)

Humid air k ha k a ( 1 − RH P sat

P 0 ) + k v RH P sat

P 0 Tsilingiris (2018)

FAM-Z02 powder k s 0 . 1115 + 2 × 10 −4 T ( ◦C ) Kakiuchi et al. (2004)

E

F

F

F

G

G

H

K

K

Table A1 (for more details, see refs. Bahrami et al. (2006) ; Song

and Yovanovich (1987) ; Bahrami et al. (2006) ).

Appendix B

Thermal conductivities of the dry air, water vapour, humid air

and FAM-Z02 powder are calculated from the equations presented

in Table B1 .

References

Alsaman, A .S. , Askalany, A .A . , Harby, K. , Ahmed, M.S. , 2017. Performance evaluation

of a solar-driven adsorption desalination-cooling system. Energy 128, 196–207 . Aristov, Y.I. , Glaznev, I.S. , Girnik, I.S. , 2012. Optimization of adsorption dynamics in

adsorptive chillers: Loose grains configuration. Energy 46 (1), 4 84–4 92 .

Bahrami, M. , Culham, J.R. , Yananovich, M.M. , Schneider, G.E. , 2006. Review of ther-mal joint resistance models for nonconforming rough surfaces. Appl. Mech. Rev.

59 (1), 1 . Bahrami, M. , Yovanovich, M.M. , Culham, J.R. , 2006. Effective thermal conductivity of

rough spherical packed beds. Int. J. Heat Mass Transf. 49 (19–20), 3691–3701 . Cabeza, L.F. , 2014. Advances in Thermal Energy Storage Systems : Methods and Ap-

plications. Woodhead Publishing . Czichos, H. , Saito, T. , Smith, L. , 2011. Springer Handbook of Metrology and Testing,

Second ed. Springer .

Dawoud, B. , Sohel, M.I. , Freni, A. , Vasta, S. , Restuccia, G. , 2011. On the effective ther-mal conductivity of wetted zeolite under the working conditions of an adsorp-

tion chiller. Appl. Therm. Eng. 31 (14–15), 2241–2246 . Do, D.D. , 1998. Adsorption Analysis: Equilibria and Kinetics, 2. Imperial College Press

Imperial College Press .



l-Sharkawy, I.I. , Abdelmeguid, H. , Saha, B.B. , 2013. Towards an optimal performanceof adsorption chillers: reallocation of adsorption/desorption cycle times. Int. J.

Heat Mass Transf. 63, 171–182 . razzica, A. , Füldner, G. , Sapienza, A. , Freni, A. , Schnabel, L. , 2014. Experimental and

theoretical analysis of the kinetic performance of an adsorbent coating compo-sition for use in adsorption chillers and heat pumps. Appl. Therm. Eng. 73 (1),

1022–1031 .

reni, A. , Bonaccorsi, L. , Calabrese, L. , Caprì, A. , Frazzica, A. , Sapienza, A. , 2015.SAPO-34 coated adsorbent heat exchanger for adsorption chillers. Appl. Therm.

Eng. 82, 1–7 . reni, A. , Dawoud, B. , Bonaccorsi, L. , Chmielewski, S. , Frazzica, A. , Calabrese, L. ,

Restuccia, G. , 2015. Characterization of zeolite-based coatings for adsorp-tion heat pumps, Cham. Springer Briefs in Applied Sciences and Technology.

Springer .

oldsworthy, M.J. , 2014. Measurements of water vapour sorption isotherms for RDsilica gel, AQSOA-Z01, AQSOA-Z02, AQSOA-Z05 and CECA zeolite 3A. Microp-

orous Mesoporous Mater 196, 59–67 . riesinger, A. , Spindler, K. , Hahne, E. , 1999. Measurements and theoretical modelling

of the effective thermal conductivity of zeolites. Int. J. Heat Mass Transf. 42 (23),4363–4374 .

auer, A. , Fischer, F. , 2011. Open adsorption system for an energy efficient dish-

washer. Chem. Ing. Tech. 83 (1–2), 61–66 . Hegazy, A .A .-H. , 1985. Thermal Joint Conductance of Conforming Rough Surfaces:

Effect of Surface Micro-Hardness Variation. University of Waterloo . Incropera, F.P. , Dewitt, D.P. , Bergman, T.L. , Lavine, A.S. , 2007. Fundamentals of Heat

and Mass Transfer, 6th ed. John Wiley & Sons . akiuchi, H. , Iwade, M. , Shimooka, S. , Ooshima, K. , 2004. Novel zeolite adsorbents

and their application for AHP and Desiccant system. In: Proceedings of the

IEA-Annex 17 Meeting. Beijing . arayacoubian, P. , Bahrami, M. , Culham, J.R. , 2005. Asymptotic solutions of effec-

tive thermal conductivity. In: 2005 ASME International Mechanical EngineeringCongress and Exposition .



http://refhub.elsevier.com/S0140-7007(18)30170-1/sbref0001




















































































ARTICLE IN PRESS

JID: JIJR [m5G; July 17, 2018;20:14 ]

K

L

L

L

M

N

P

P

R

R

R

R

R

R

R

S

S

S

S

S

T

T

T

VW

Y

Y

Z

aviany, M. , 1995. Principles of Heat Transfer in Porous Media, Second Ed. Springer,New York .

i, G. , Hwang, Y. , Radermacher, R. , 2014. Experimental investigation on energy andexergy performance of adsorption cold storage for space cooling application. Int.

J. Refrig. 44, 23–35 . i, X.H. , Hou, X.H. , Zhang, X. , Yuan, Z.X. , 2015. A review on development of ad-

sorption cooling–novel beds and advanced cycles. Energy Convers. Manag. 94,221–232 .

uikov, A.V. , Shashkov, A.G. , Vasiliev, L.L. , Fraiman, Y.E. , 1968. Thermal conductivity

of porous systems. Int. J. Heat Mass Transf. 11, 117–140 . ohammed, R.H. , Mesalhy, O. , Elsayed, M.L. , Chow, L.C. , 2017. Novel compact bed

design for adsorption cooling systems: parametric numerical study. Int. J. Refrig.80, 238–251 .

’Tsoukpoe, K.E. , Restuccia, G. , Schmidt, T. , Py, X. , 2014. The size of sorbents inlow pressure sorption or thermochemical energy storage processes. Energy 77,

983–998 .

alomba, V. , Vasta, S. , Freni, A. , 2017. Experimental testing of AQSOA FAM Z02/wateradsorption system for heat and cold storage. Appl. Therm. Eng. 124, 967–974 .

istocchini, L. , Garone, S. , Motta, M. , 2016. Air dehumidification by cooled adsorp-tion in silica gel grains. Part I: experimental development of a prototype. Appl.

Therm. Eng. 107, 888–897 . amzy K, A. , Ashok Babu, T.P. , Kadoli, R. , 2011. Semi-analytical method for heat and

moisture transfer in packed bed of silica gel. Int. J. Heat Mass Transf. 54 (4),

983–993 . ezk, A.R.M. , Al-Dadah, R.K. , 2012. Physical and operating conditions effects on silica

gel/water adsorption chiller performance. Appl. Energy 89 (1), 142–149 . ezk, A. , Al-Dadah, R.K. , Mahmoud, S. , Elsayed, A. , 2013. Effects of contact resistance

and metal additives in finned-tube adsorbent beds on the performance of silicagel/water adsorption chiller. Appl. Therm. Eng. 53 (2), 278–284 .

iffel, D.B. , Wittstadt, U. , Schmidt, F.P. , Núñez, T. , Belo, F.A . , Leite, A .P.F. , Ziegler, F. ,

2010. Transient modeling of an adsorber using finned-tube heat exchanger. Int.J. Heat Mass Transf. 53 (7–8), 1473–1482 .

ouhani, M. , Bahrami, M. , 2018. Effective thermal conductivity of packed bed adsor-bers : Part 2 – theoretical model. Int. J. Heat Mass Transf. .

ouhani, M. , Huttema, W. , Bahrami, M. , 2016. Heat flow meter measurement of thethermal conductivity and contact resistance of FAM AQSOA-Z02 pellets between

aluminium plates. In: Proceedings of the Fourth International Symposium on

Innovative Materials for Processes in Energy Systems (IMPRES2016) .



ouhani, M. , Huttema, W. , Bahrami, M. , 2018. Effective thermal conductivity ofpacked bed adsorbers: Part 1–Experimental study. Int. J. Heat Mass Transf. 123,

1204–1211 . arwar, M.K. , Majumdar, P. , 1995. Thermal conductivity of wet composite porous

media. Heat Recover. Syst. CHP 15 (4), 369–381 . chreiber, H. , Graf, S. , Lanzerath, F. , Bardow, A. , 2015. Adsorption thermal energy

storage for cogeneration in industrial batch processes: experiment, dynamicmodeling and system analysis. Appl. Therm. Eng. 89, 4 85–4 93 .

harafian, A. , Fayazmanesh, K. , McCague, C. , Bahrami, M. , 2014. Thermal conduc-

tivity and contact resistance of mesoporous silica gel adsorbents bound withpolyvinylpyrrolidone in contact with a metallic substrate for adsorption cooling

system applications. Int. J. Heat Mass Transf. 79, 64–71 . ong, S. , Yovanovich, M.M. , 1987. Correlation of thermal accomodation coefficient

for engineering surfaces. In: Proceedings of the Twenty Fourth National HeatTransfer Conference and Exhibition, pp. 107–116 .

troud, D. , 1998. The effective medium approximations: some recent developments.

Superlattices Microstruct. 23 (3), 567–573 . ien, C.L. , Vafai, K. , 1978. Statistical upper and lower bounds of effective thermal

conductivity of fibrous insulation. In: Proceedings of the Second AIAA/ASMEThermophysics And Heat Transfer Conference .

silingiris, P.T. , 2018. Review and critical comparative evaluation of moist air ther-mophysical properties at the temperature range between 0 and 100 °C for Engi-

neering Calculations. Renew. Sustain. Energy Rev. 83, 50–63 .

sotsas, E. , Martin, H. , 1987. Thermal conductivity of packed beds: a review. Chem.Eng. Process. 22 (1), 19–37 .

DI Heat Atlas, Second ed. Springer, 2010. agner, W. , Kretzschmar, H.-J. , 2008. International SteamTables–Properties Ofwa-

ter and Steam Based On the Industrial Formulation IAPWS-IF97, Second ed.Springer-Verlag, Berlin .

ovanovich , 2003. Thermal spreading and contact resistances. In: Bejan, A., Kraus, D.

(Eds.), Heat Transfer Handbook. John Wiley and Sons Inc., New York . u, N. , Wang, R.Z. , Wang, L.W. , 2013. Sorption thermal storage for solar energy. Prog.

Energy Combust. Sci. 39 (5), 489–514 . hu, D. , Wang, S. , 2002. Experimental investigation of contact resistance in adsorber

of solar adsorption refrigeration. Sol. Energy 73 (3), 177–185 .











































































































international journal of refrigerationmbahrami/pdf/2018/thermal conductivity... · rezk and...

Documents